It also returns the numerator, AllpassNum,
and the denominator, AllpassDen, of the allpass
mapping filter. The prototype lowpass filter is given with a numerator
specified by B and a denominator specified by A.

Parameter N also specifies the number of
replicas of the prototype filter created around the unit circle after
the transformation. This transformation effectively places N features
of an original filter, located at frequencies Wo1,...,WoN,
at the required target frequency locations, Wt1,...,WtM.

Relative positions of other features of an original filter are
the same in the target filter for the Nyquist mobility and are reversed
for the DC mobility. For the Nyquist mobility this means that it is
possible to select two features of an original filter, F1 and
F2, with F1 preceding
F2. Feature F1 will
still precede F2 after the transformation.
However, the distance between F1 and F2 will
not be the same before and after the transformation. For DC mobility
feature F2 will precede F1 after
the transformation.

Choice of the feature subject to this transformation is not
restricted to the cutoff frequency of an original lowpass filter.
In general it is possible to select any feature; e.g., a stopband
edge, DC, the deep minimum in the stopband, or other ones. The only
condition is that the features must be selected in such a way that
when creating N bands around the unit circle, there
will be no band overlap.

This transformation can also be used for transforming other
types of filters; e.g., notch filters or resonators can be easily
replicated at a number of required frequency locations. A good application
would be an adaptive tone cancellation circuit reacting to the changing
number and location of tones.